NEW YORK (CNN) -- The daughter of a man who died after falling four stories at Shea Stadium said her father was not sliding down the escalator when the accident happened, as police reported.

A statement from the New York Police Department on Tuesday said witnesses saw 36-year-old Antonio Nararainsami of Brooklyn sitting on the banister of the escalator when he lost his balance and fell.

Nararainsami's daughter, Emily, told CNN affiliate WABC on Tuesday that her father was walking down the escalator, not sliding on its banister, as fans left the stadium after the New York Mets-Washington Nationals game. She said she and another relative saw what happened.

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"He wasn't moving or nothing; he was just walking down. I guess he tried to say something to us or something, and I guess he just lost his balance and flipped over," she said.

Nararainsami died at Booth Memorial Hospital about 25 minutes after the 10 p.m. incident.